Personally I suspect it this. I’m not 100% of how exactly f.lux etc works, but I’ve always assumed they work by applying a full screen filter that basically just reduces the Blue channel values, and possibly tweaks the other channels a tad to keep things looking reasonable.
Of course on of the side effects of doing that would be reducing the total amount of light your screen emits, and I assume this has to be true, because red and green would end up clipping if they were boosted to keep the light output the same.
As the app applies removes more blue, it further dims the image, and when you turn it off if restores all the channels, which also increases the screens total light output. And you basically get the same effect as opening the curtains in the morning (assuming your working in darkish room), with the resulting eye discomfort while they adjust to the increased brightness.
Best way to test this would be use the apps, and modulate the screen backlight to compensate for the reduced blue level, so the total lux emitted remains constant. Then switching back and forth would let you figure out is your eyes are responding to the blue, or just the total light level.
I don't really care whether it's harmful or not, after all the amount of time I spend at the computer is harmful too.
I've never experienced any bad side effects form that. When I'm tired I can always sleep instantly.
Funny enough I don't like bluish light besides on computer screens. All my lights are dimmed, and I prefer them being kind of orange. Actually my eyes hurt when being in places that use bright cold lights.
That makes the contrast (especially at night) between my computer screens and the ambient light quite significant. The screens seem the brightest lights in the room. Even they are also dimmed.
For the matter at hand I think there's one important observation to make: Most screens are just way too bright in default settings!¹ I usually dim screens to at least ~50%; when it's a bright one even down to ~30%. Not only that my eyes start to hurt after a short time looking at a screen in factory settings I get every time even severe headache after some hours looking at such a thing.
Most people I know don't dim screens. They like it as bright a possible as it makes the color experience best (and you don't need to dim the light in the room to be able to see something on the screen–especially during day and when there is sunshine around). The screen manufacturers also picked that up: Every new screen has an even more extreme maximal brightness than the previous models. It seems to be the "loudness war" of screen manufacturers.
A screen with warmer colors is less bright than a screen with cold colors (as the screens usually don't adjust brightness at the same time when fiddling with the colors). The back-light of a screen has a quite extreme cold color so making the screen more warm filters more of the back-light and makes the screen less bright as a result.
So if I would have to guess why some people experience positive effects from "redshift"-tools I would bet the effect is actually only related to screen brightness and has nothing to do with the color as such.
Whoever came up with this "redshift" theory was overthinking things, imho: It's true that the natural light gets more warm in the evening (as it is also in the morning… ;-)). But it gets also darker when night comes! That's actually the significant phenomenon in my opinion.
¹ Just try to look for some time into a 160W light-bulb… Try also a 40W model instead.
Due to me working primarily as a developer, i don't always need good color accuracy, so my current settings of screen color warmth are the following:
In addition to that, i have a few smart lightbulbs that change to a more red color as the night approaches and gently dim more and more when i don't need to do any reading and just have to walk around the house. Subjectively, i'd say that it's better for me being able to fall asleep and experience a bit less eye strain (though admittedly, using a computer late into the night is never a good idea).Perhaps the discomfort is just because of eyes having a hard time adjusting to noticeably different lighting conditions, but maybe there's more to it.